Multiple-Input Multiple-Output (MIMO) is a key element of the air interface for high-speed wireless communications for many wireless communication technologies such as Long Term Evolution (LTE) and High Speed Packet Access (HSPA). MIMO can use the diversity in the channel to provide multiplexing gain by enabling the simultaneous transmission of multiple streams known as layers. Denoting the number of transmit antennas, receive antennas, and layers by NT, NR, and R, respectively, R is bounded above by the minimum of NT and NR. One possible implementation of MIMO uses a precoder, often expressed mathematically as a left-multiplication of a layer signal vector (R×1) by a precoding matrix (NT×R), which is chosen from a codebook, i.e., a pre-defined set of matrices. Each precoding matrix is indexed by a rank indicator (RI) and a precoding matrix indicator (PMI). The r-th column vector of the precoding matrix represents the antenna spreading weight of the r-th layer. The precoding matrix usually consists of linearly independent columns, and thus R is referred to as the rank of the codebook. One purpose of this kind of precoder is to match the precoding matrix with the channel state information (CSI) so as to increase the received signal power and also to some extent reduce inter-layer interference, thereby improving the signal-to-interference-plus-noise-ratio (SINR) of each layer. Consequently, the precoder selection requires the transmitter to know the channel properties and, generally speaking, the more accurate the CSI, the better the precoder matches.
In the case of the 3GPP LTE uplink (UL), the receiver (NodeB) makes the precoder selection, so there is no need to feed channel information back to the transmitter. (“Precoder selection” includes not only rank selection, but also precoding matrix selection throughout this disclosure.) Instead, it is necessary for the receiver to obtain channel information, which can usually be facilitated by transmitting a known signal, in the case of LTE UL, the Demodulation Reference Signal (DM-RS) and the Sounding Reference Signal (SRS). Both DM-RS and SRS are defined in the frequency domain and are derived from the Zadoff-Chu sequence. However, since the DM-RS is precoded while the SRS is not precoded, the channel information obtained from DM-RS is the equivalent channel that the R layers experience, not the physical channel that the NT antennas experience, Mathematically, letting the NR×NT physical channel matrix, the NT×R precoding matrix, and the NR×R equivalent channel be denoted by H, W and E, respectively, it follows that:E=HDWt  (1)where D is the NT×NT diagonal matrix whose diagonal elements represent a phase shift introduced by the transmitter chains. As will be seen later, the phase shift is not uniform and need not be constant. In detail, the i-th diagonal element is given as di=exp(jφi). As will be shown in the next section, the phase shift may result in significant performance loss, when the relative phase between the transmitter chains changes from one phase of transmission to another, for example from SRS to the Physical Uplink Shared Channel (PUSCH).
Using the above notation, the equivalent channels for PUSCH, DM-RS and SRS denoted by EPUSCH, EDMRS and ESRS can be expressed as:EPUSCH=HW EDMRS=HW HSRS=HD.  (2)
Here it is assumed that there is no channel variation among PUSCH, DM-RS, and SRS, and D is set to the identity matrix for PUSCH and DM-RS without loss of generality due to the fact that only relative phase variations are of concern. Note that it is also assumed that PUSCH and DM-RS experience the same channel. Also note that HSRS in equation (2) is directly obtained from SRS, and based on HSRS, the equivalent channel ESRS as a function of a hypothesized precoder W can be obtained as ESRS=HSRSW.
Precoder selection is preferably based on SRS, since it is more easily done with complete knowledge of the channel, i.e., the physical channel, HD in equation (2). Based on the physical channel estimated based on SRS, the best transmission mode is chosen by the receiver and sent back to the transmitter. One of the criteria for selecting the transmission mode is to maximize the throughput. For example, the effective SNR is calculated for each precoder, i.e., each selection of the rank and precoder matrix, the relevant throughput is calculated, and the precoder that maximizes the throughput is selected. Consequently, it is easily understood that precoder selection is subject to inter-antenna imbalance variation between measurement period (SRS) and actual data transmission period (PUSCH).